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At least 37 records · Page 2

Sensitivity of Latent Heating Profiles to Environmental Conditions: Implications for TRMM and Climate Research

The Tropical Rainfall Measuring Mission (TRMM) as a part of NASA's Earth System Enterprise is the first mission dedicated to measuring tropical rainfall through microwave and visible sensors, and includes the first spaceborne rain radar. Tropical rainfall comprises two-thirds of global rainfall. It is also the primary distributor of heat through the atmosphere's circulation. It is this circulation that defines Earth's weather and climate. Understanding rainfall and its variability is crucial to understanding and predicting global climate change. Weather and climate models need an accurate assessment of the latent heating released as tropical rainfall occurs. Currently, cloud model-based algorithms are used to derive latent heating based on rainfall structure. Ultimately, these algorithms can be applied to actual data from TRMM. This study investigates key underlying assumptions used in developing the latent heating algorithms. For example, the standard algorithm is highly dependent on a system's rainfall amount and structure. It also depends on an a priori database of model-derived latent heating profiles based on the aforementioned rainfall characteristics. Unanswered questions remain concerning the sensitivity of latent heating profiles to environmental conditions (both thermodynamic and kinematic), regionality, and seasonality. This study investigates and quantifies such sensitivities and seeks to determine the optimal latent heating profile database based on the results. Ultimately, the study seeks to produce an optimized latent heating algorithm based not only on rainfall structure but also hydrometeor profiles.

Shepherd, J. Marshall↗

Latent Heating Retrievals Using the TRMM Precipitation Radar: A Multi-Seasonal Study

Rainfall is a key link in the hydrologic cycle and is a primary heat source for the atmosphere. The vertical distribution of latent heat release, which is accompanied by rainfall, modulates the large-scale circulations of the tropics and in turn can impact midlatitude weather. This latent heat release is a consequence of phase changes between vapor, liquid, and solid water. Present largescale weather and climate models can simulate latent heat release only crudely, thus reducing their confidence in predictions on both global and regional scales. This paper represents the first attempt to use NASA Tropical Rainfall Measuring Mission (TRMM) rainfall information to estimate the four-dimensional structure of global monthly latent heating profiles over the global tropics from December 1997 to October 2000. The Goddard Convective-Stratiform. Heating (CSH) algorithm and TRMM precipitation radar data are used for this study. We will examine and compare the latent heating structures between 1997-1998 (winter) ENSO and 1998-2000 (non-ENSO). We will also examine over the tropics. The seasonal variation of heating over various geographic locations (i.e., oceanic vs continental; Indian oceans vs west Pacific; Africa vs S. America) will be also examined and compared. In addition, we will examine the relationship between latent heating (max heating level) and SST. The period of interest also coincides with several TRMM field campaigns that recently occurred over the South China Sea in 1998 (SCSMEX), Brazil in 1999 (TRMM-LBA), and in the central Pacific in 1999 (KWAJEX). Sounding diagnosed Q1 budgets from these experiments could provide a means of validating the retrieved profiles of latent heating from the CSH algorithm.

Tao, Wei-Kuo↗

Tropical Gravity Wave Momentum Fluxes and Latent Heating Distributions

Recent satellite determinations of global distributions of absolute gravity wave (GW) momentum fluxes in the lower stratosphere show maxima over the summer subtropical continents and little evidence of GW momentum fluxes associated with the intertropical convergence zone (ITCZ). This seems to be at odds with parameterizations forGWmomentum fluxes, where the source is a function of latent heating rates, which are largest in the region of the ITCZ in terms of monthly averages. The authors have examined global distributions of atmospheric latent heating, cloud-top-pressure altitudes, and lower-stratosphere absolute GW momentum fluxes and have found that monthly averages of the lower-stratosphere GW momentum fluxes more closely resemble the monthly mean cloud-top altitudes rather than the monthly mean rates of latent heating. These regions of highest cloud-top altitudes occur when rates of latent heating are largest on the time scale of cloud growth. This, plus previously published studies, suggests that convective sources for stratospheric GW momentum fluxes, being a function of the rate of latent heating, will require either a climate model to correctly model this rate of latent heating or some ad hoc adjustments to account for shortcomings in a climate model's land-sea differences in convective latent heating.

momentum↗

$\text{GPLaSDI}$: Gaussian Process-based interpretable Latent Space Dynamics Identification through deep autoencoder

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating and solving the ODE system in the reduced latent space, fast and accurate ROM predictions can be made by feeding the predicted latent space dynamics into the decoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the ROM predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. Here we demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

97 MATHEMATICS AND COMPUTING↗

Towards interpretable Cryo-EM: disentangling latent spaces of molecular conformations

Molecules are essential building blocks of life and their different conformations (i.e., shapes) crucially determine the functional role that they play in living organisms. Cryogenic Electron Microscopy (cryo-EM) allows for acquisition of large image datasets of individual molecules. Recent advances in computational cryo-EM have made it possible to learn latent variable models of conformation landscapes. However, interpreting these latent spaces remains a challenge as their individual dimensions are often arbitrary. The key message of our work is that this interpretation challenge can be viewed as an Independent Component Analysis (ICA) problem where we seek models that have the property of identifiability. That means, they have an essentially unique solution, representing a conformational latent space that separates the different degrees of freedom a molecule is equipped with in nature. Thus, we aim to advance the computational field of cryo-EM beyond visualizations as we connect it with the theoretical framework of (nonlinear) ICA and discuss the need for identifiable models, improved metrics, and benchmarks. Moving forward, we propose future directions for enhancing the disentanglement of latent spaces in cryo-EM, refining evaluation metrics and exploring techniques that leverage physics-based decoders of biomolecular systems. Moreover, we discuss how future technological developments in time-resolved single particle imaging may enable the application of nonlinear ICA models that can discover the true conformation changes of molecules in nature. The pursuit of interpretable conformational latent spaces will empower researchers to unravel complex biological processes and facilitate targeted interventions. This has significant implications for drug discovery and structural biology more broadly. More generally, latent variable models are deployed widely across many scientific disciplines. Thus, the argument we present in this work has much broader applications in AI for science if we want to move from impressive nonlinear neural network models to mathematically grounded methods that can help us learn something new about nature.

59 BASIC BIOLOGICAL SCIENCES↗

Latent Viruses: A Space Travel Hazard??

A major issue associated with long-duration space flight is the possibility of infectious disease causing an unacceptable medical risk to crew members. Our proposal is designed to gain information that addresses several issues outlined in the Immunology/Infectious disease critical path. The major hypothesis addressed is that space flight causes alterations in the immune system that may allow latent viruses which are endogenous in the human population to reactivate and shed to higher levels than normal which can affect the health of crew members during a long term space-flight mission. We will initially focus our studies on the human herpesviruses and human polyomaviruses which are important pathogens known to establish latent infections in the human population. Both primary infection and reactivation from latent infection with this group of viruses can cause a variety of illnesses that result in morbidity and occasionally mortality of infected individuals. Effective vaccines exist for only one of the eight known human herpesviruses and the vaccine itself can still reactivate from latent infection. Available antivirals are of limited use and are effective against only a few of the human herpesviruses. Although most individuals display little if any clinical consequences from latent infection, events which alter immune function such as immunosuppressive therapy following solid organ transplantation are known to increase the risk of developing complications as a result of latent virus reactivation. This proposal will measure both the frequency and magnitude of viral shedding and genome loads in the blood from humans participating in activities that serve as ground based models of space flight conditions. Our initial goal is to develop sensitive quantitative competitive PCR- based assays (QC-PCR) to detect the herpesvirus Epstein-Barr virus (EBV), and the polyomaviruses SV40, BKV, and JCV. Using these assays we will establish baseline patterns of viral genome load in the blood and viral shedding from normal volunteers in a longitudinal study over I year in length. As a comparison, we will measure patterns of viral genome loads and shedding from individuals who are severely immunosuppressed, in whom herpesvirus reactivation or primary infection with a herpesvirus is known to cause complications. In addition, we will proceed to testing ground based analogs in collaboration with Dr. Duane Pierson (Lyndon B. Johnson Space Center). This will include measuring samples obtained from individuals living and working in the extreme environment of Antarctica. We expect to detect viral shedding or reactivation from most of the test groups, although the magnitude of shedding or reactivation cannot be predicted. The data accumulated from studies in this proposal should allow us to evaluate whether events that simulate certain aspects of space flight reactivate viral infections severe enough in nature that they may compromise the success of long-term space flight missions. These studies will also provide a foundation to monitor viral reactivation and shedding from crew members participating in actual space flight missions. We will present data showing the establishment of our QC-PCR assay for detection of EBV.

Ling, P. D.↗

Vertical Profiles of Latent Heat Release over the Global Tropics using TRMM Rainfall Products from December 1997 to November 2002

NASA Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) derived rainfall information will be used to estimate the four-dimensional structure of global monthly latent heating and rainfall profiles over the global tropics from December 1997 to November 2000. Rainfall, latent heating and radar reflectivity structures between El Nino (DJF 1997-98) and La Nina (DJF 1998-99) will be examined and compared. The seasonal variation of heating over various geographic locations (i.e., oceanic vs continental, Indian ocean vs west Pacific, Africa vs. S. America ) will also be analyzed. In addition, the relationship between rainfall, latent heating (maximum heating level), radar reflectivity and SST is examined and will be presented in the meeting. The impact of random error and bias in stratiform percentage estimates from PR on latent heating profiles is studied and will also be presented in the meeting. The Goddard Cumulus Ensemble Model is being used to simulate various mesoscale convective systems that developed in different geographic locations. Specifically, the model estimated rainfall, radar reflectivity and latent heating profiles will be compared to observational data collected from TRMM field campaigns over the South China Sea in 1998 (SCSMEX), Brazil in 1999 (TRMM-LBA), and the central Pacific in 1999 (KWAJEX). Sounding diagnosed heating budgets and radar reflectivity from these experiments can provide the means to validate (heating product) as well as improve the GCE model. Review of other latent heating algorithms will be discussed in the workshop.

Tao, W.-K.↗

Distributed non-negative matrix factorization with determination of the number of latent features

The holistic analysis and understanding of the latent (that is, not directly observable) variables and patterns buried in large datasets is crucial for data-driven science, decision making and emergency response. Such exploratory analyses require devising unsupervised learning methods for data mining and extraction of the latent features, and non-negative matrix factorization (NMF) is one of the prominent such methods. NMF is based on compute-intense non-convex constrained minimization, which, for large datasets requires fast and distributed algorithms. However, current parallel implementations of NMF fail to estimate the number of latent features. In practice, identifying these features is both difficult and significant for pattern recognition and latent feature analysis, especially for large dense matrices. Here, we introduce a distributed NMF algorithm coupled with distributed custom clustering followed by a stability analysis on dense data, which we call DnMFk, to determine the number of latent variables. The results on synthetic data and the classical Swimmer data set demonstrate the accuracy of model determination while scaling nearly linearly across multiple processors for large data. Further, we employ DnMFk to determine the number of hidden features from a terabyte matrix.

97 MATHEMATICS AND COMPUTING↗

Weak-form latent space dynamics identification

Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the LaSDI (Latent Space Dynamics Identification) algorithm, a recently developed data-driven reduced order modeling technique. We introduce a weak form-based version WLaSDI (Weak-form Latent Space Dynamics Identification). WLaSDI first compresses data, then projects onto the test functions and learns the local latent space models. Notably, WLaSDI demonstrates significantly enhanced robustness to noise. With WLaSDI, the local latent space is obtained using weak-form equation learning techniques. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form guarantees a robust and precise latent space recovery, hence allowing for a fast, robust, and accurate simulation. We demonstrate the efficacy of WLaSDI vs. LaSDI on several common benchmark examples including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in the case of 1D inviscid Burgers' simulations with the addition of up to 100% Gaussian white noise, the relative error remains consistently below 6% for WLaSDI, while it can exceed 10,000% for LaSDI. Similarly, for radial advection simulations, the relative errors stay below 15% for WLaSDI, in stark contrast to the potential errors of up to 10,000% with LaSDI. Moreover, speedups of several orders of magnitude can be obtained with WLaSDI. For example applying WLaSDI to 1D Burgers' yields a 140X speedup compared to the corresponding full order model.

97 MATHEMATICS AND COMPUTING↗

Characterization of latent image of electron beam resist via critical-dimension resonant soft X-ray scattering

Metrology plays a crucial role in semiconductor manufacturing by providing accurate and precise measurement and characterization of critical parameters. With the development of high-resolution extreme ultraviolet lithography (EUVL) processes, critical dimensions are shrinking to sub-10 nm. Resist materials encounter the challenge of providing heightened sensitivity and a handle on exacerbating stochastic variations. A comprehensive understanding of the chemical profile of the latent image is pivotal for mitigating stochastic effects and optimizing pattern quality. However, the subtle differences in chemistry between the exposed and unexposed regions of the resists make it extremely challenging to characterize the latent images with sub-nanometer precision. Here, we develop the metrology with critical-dimension resonant soft X-ray scattering (CD-RSoXS) to probe the chemical profiles of latent images stored in resist after exposure. The combination of absorption spectroscopy and enhanced scattering contrast makes it possible to characterize the subtle structural and chemical variations in the latent image. Moreover, the results of the measurements are compared with the simulations with a finite element method–based Maxwell solver to extract a detailed profile of the latent and developed images. We demonstrate that the CD-RSoXS technique can provide valuable insights into the high spatial resolution and local chemical sensitivity simultaneously, which is crucial to understanding the resolution limits and stochastic effects in EUVL processes.

36 MATERIALS SCIENCE↗

tLaSDI: Thermodynamics-informed latent space dynamics identification

Here we propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

97 MATHEMATICS AND COMPUTING↗

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗

A neural network for determination of latent dimensionality in Nonnegative Matrix Factorization

Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy datasets with applications in data mining, text recognition, dimension reduction, face recognition, anomaly detection, blind source separation, and many other fields. An important input for NMF is the latent dimensionality of the data, that is, the number of hidden features, K, present in the explored dataset. Unfortunately, and this quantity is rarely known a priori. The existing methods for determining latent dimensionality, such as Automatic Relevance Determination (ARD), are mostly heuristic and utilize different characteristics to estimate the number of hidden features. However, all of them require human presence to make a final determination of K. Here we utilize a supervised machine learning approach in combination with a recent method for model determination, called NMFk, to determine the number of hidden features automatically. NMFk performs a set of NMF simulations on an ensemble of matrices, obtained by bootstrapping the initial dataset, and estimates which K produces stable groups of latent features that reconstruct the initial dataset well. We then train a Multi-Layter Perceptron (MLP) classifier network to determine the correct number of latent features utilizing the statistics and characteristics of the NMF solution, obtained from NMFk. In order to train the MLP classifier, a training set of 58,660 matrices with predetermined latent features were factorized with NMFk. The MLP classifier in conjunction with NMFk maintains a greater than 95% success rate when applied to a held out test set. Additionally, when applied to two well-known benchmark datasets, the swimmer and MIT face data, NMFk/MLP correctly recovers the established number of hidden features. Finally, we compare the accuracy of our method to the ARD, AIC and Stability-based methods.

97 MATHEMATICS AND COMPUTING↗

Thermodynamics-informed latent space dynamics identification

This software showcases a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

Cheung, Siu Wun↗

Bayesian inference of structured latent spaces from neural population activity with the orthogonal stochastic linear mixing model

The brain produces diverse functions, from perceiving sounds to producing arm reaches, through the collective activity of populations of many neurons. Determining if and how the features of these exogenous variables (e.g., sound frequency, reach angle) are reflected in population neural activity is important for understanding how the brain operates. Often, high-dimensional neural population activity is confined to low-dimensional latent spaces. However, many current methods fail to extract latent spaces that are clearly structured by exogenous variables. This has contributed to a debate about whether or not brains should be thought of as dynamical systems or representational systems. Here, we developed a new latent process Bayesian regression framework, the orthogonal stochastic linear mixing model (OSLMM) which introduces an orthogonality constraint amongst time-varying mixture coefficients, and provide Markov chain Monte Carlo inference procedures. We demonstrate superior performance of OSLMM on latent trajectory recovery in synthetic experiments and show superior computational efficiency and prediction performance on several real-world benchmark data sets. We primarily focus on demonstrating the utility of OSLMM in two neural data sets: μ ECoG recordings from rat auditory cortex during presentation of pure tones and multi-single unit recordings form monkey motor cortex during complex arm reaching. We show that OSLMM achieves superior or comparable predictive accuracy of neural data and decoding of external variables (e.g., reach velocity). Most importantly, in both experimental contexts, we demonstrate that OSLMM latent trajectories directly reflect features of the sounds and reaches, demonstrating that neural dynamics are structured by neural representations. Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale biological time-series datasets.

59 BASIC BIOLOGICAL SCIENCES↗

The algebraic theory of latent projectors in lambda matrices

Multivariable systems such as a finite-element model of vibrating structures, control systems, and large-scale systems are often formulated in terms of differential equations which give rise to lambda matrices. The present investigation is concerned with the formulation of the algebraic theory of lambda matrices and the relationship of latent roots, latent vectors, and latent projectors to the eigenvalues, eigenvectors, and eigenprojectors of the companion form. The chain rule for latent projectors and eigenprojectors for the repeated latent root or eigenvalues is given.

Denman, E. D.↗

Vertical Profiles of Latent Heat Release Over the Global Tropics using TRMM Rainfall Products from December 1997 to November 2001

NASA Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) derived rainfall information will be used to estimate the four-dimensional structure of global monthly latent heating and rainfall profiles over the global tropics from December 1997 to November 2000. Rainfall, latent heating and radar reflectivity structures between El Nino (DJF 1997-98) and La Nina (DJF 1998-99) will be examined and compared. The seasonal variation of heating over various geographic locations (i.e., oceanic vs continental, Indian ocean vs west Pacific, Africa vs S. America) will also be analyzed. In addition, the relationship between rainfall, latent heating (maximum heating level), radar reflectivity and SST is examined and will be presented in the meeting. The impact of random error and bias in stratiform percentage estimates from PR on latent heating profiles is studied and will also be presented in the meeting. The Goddard Cumulus Ensemble Model is being used to simulate various mesoscale convective systems that developed in different geographic locations. Specifically, the model estimated rainfall, radar reflectivity and latent heating profiles will be compared to observational data collected from TRMM field campaigns over the South China Sea in 1998 (SCSMEX), Brazil in 1999 (TRMM-LBA), and the central Pacific in 1999 (KWAJEX). Sounding diagnosed heating budgets and radar reflectivity from these experiments can provide the means to validate (heating product) as well as improve the GCE model.

Tao, W.-K.↗